$$\frac{7+4i}{4-3i}$$ write the complex number in standard form

(7+4i)(4+3i)/(16+9) =(28 + 21i+ 16i - 12)/25 = (16 + 37i)/25

$$\frac{7+4i}{4-3i}=\frac{7+4i}{4-3i}\cdot\frac{4+3i}{4+3i}=\frac{28+21i+16i+12i^2}{4^2-(3i)^2}=\frac{28+37i-12}{16-9i^2}\\\\=\frac{16+37i}{16+9}=\frac{16+37i}{25}=\boxed{\frac{16}{25}+\frac{37}{25}i}$$

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